Condition-Based Maintenance for Queues With Degrading Servers

International Journal of Industrial and Systems Engineering, 2014

The Markov model is developed to explore the performance analysis of a state dependent working vacation queueing system with interdependent rates. The server is subjected to breakdown randomly while providing services. When a breakdown occurs, the server is immediately sent to the repair station where the repairman takes a setup time before starting the repair. The failed server is inspected by the repairman and if there is minor problem, the server is repaired and is sent back to the service station with probability q. If some major fault is diagnosed during inspection, the server requires second phase of repair with probability p = 1-q. The matrix geometric method is applied to obtain the queue size distribution and other performance indices such as throughput, expected delay time, etc. Various performance measures are computed for varying values of system parameters to facilitate the sensitivity analysis by taking a numerical illustration.

Fourth International Conference on Advances in Information Processing and Communication Technology - IPCT 2016, 2016

We consider an M X /G/1 queuing system with breakdown and repairs, where batches of customers are assumed to arrive in the system according to a compound poisson process. While the server is being repaired, the customer in service either remains the service position or enters a service orbit and keeps returning, after repair the server must wait for the customer to return. The server is not allowed to accepte new customers until the customer in service leaves the system. We find a stability condition for this system. In the steady state the joint distribution of the server state and queue length is obtained, and some performance mesures of the system, such as the mean number of customers in the retrial queue and waiting time, and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures. Keywords-batch arrival, break down, repair. I. Introduction Retrial queuing systems have been widely used to model many practical problems arising in telephone switching systems, telecommunication networks, and computer systems. The main characteristic of these queues is that a customer who find the sever busy upon arrival joins the retrial group called orbit to repeat his request for service after some random time. For a systematic account of the fundamental methods and results on this topic the reader can refer to the survey papers of (

Computers & Industrial Engineering, 2009

We consider the maintenance of single server queues in which the deterioration of a server is subject to random shocks. Shock arrivals deteriorate the server by a random amount. A maintenance policy is proposed whereby the server is repaired whenever its state is above a specified maintenance level. We present the system size distribution and sojourn time distribution. We derive the long run average cost, considering holding cost and repair cost. We analyze the proposed maintenance policy based on the cost analysis.

Applied Mathematical Modelling, 2009

This paper deals with the steady-state behaviour of an M/G/1 queue with an additional second phase of optional service subject to breakdowns occurring randomly at any instant while serving the customers and delayed repair. This model generalizes both the classical M/G/1 queue subject to random breakdown and delayed repair as well as M/G/1 queue with second optional service and server breakdowns. For this model, we first derive the joint distributions of state of the server and queue size, which is one of chief objectives of the paper. Secondly, we derive the probability generating function of the stationary queue size distribution at a departure epoch as a classical generalization ofPollaczek-Khinchin formula. Next, we derive Laplace Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measures and reliability indices of this model. Choudhury and Paul [5] investigated such a model under Bernoulli feedback mechanism. In this context Krishnakumar and Arivudainambi in [6] obtained the explicit expression for transient probabilities for this type of finite capacity model M/G/1/1 Bernoulli feedback queue and M/G/1/1 queue with unreliable server . Recently, Wang [8] investigated such a model with the assumption that the server is subject to breakdowns and repairs, and some critical reliability indices are obtained. More recently, Ke [9] extended the result for a multi-optional service system where concept of setup time is also introduced.

Quality Technology & Quantitative Management, 2017

In this paper, we study the steady state behaviour of an M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server's breakdowns occurring randomly at any instant while serving the customers and delayed repair. We assume that customers arrive to the system according to a Poisson process with rate 'λ' and the server provides two types of general heterogeneous service. At the beginning of a service, a customer has the option to choose any one type of service. After completion of either type of service, the customer has the further option to repeat the same type of service. For this model, we first derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, which is one of the objectives of this paper. Secondly, we derive the probability generating function of the stationary queue size distribution at departure epoch. Next, we derive Laplace-Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measure and reliability indices of this model.

This paper studies an M/G/1 repairable queueing system with multiple vacations and N-policy, in which the service station is subject to occasional random breakdowns. When the service station breaks down, it is repaired by a repair facility. Moreover, the repair facility may fail during the repair period of the service station. The failed repair facility resumes repair after completion of its replacement. Under these assumptions, applying a simple method, the probability that the service station is broken, the rate of occurrence of breakdowns of the service station, the probability that the repair facility is being replaced and the rate of occurrence of failures of the repair facility along with other performance measures are obtained. Following the construction of the long-run expected cost function per unit time, the direct search method is implemented for determining the optimum threshold N* that minimises the cost function.

This paper considers a queue, consisting of a Poisson input stream and a server. The server is subject to breakdowns. The times to failure of the server follows exponential distribution. The failed server requires repair at a facility, which has an unreliable repair crew. The repair times of the failed server follows exponential distribution, but the repair crew also subjects to breakdown when it is repairing. The times to failure of the repair crew is also assumed to be exponentially distributed. This paper obtains the steady-state performance of the queuewith server breakdowns and interrupted repairs.

Communications in Statistics - Theory and Methods, 2019

This article deals with the N-policy with setup time of an unreliable M X /G/1 queue provides two types of general heterogeneous service under optional repeated service and delayed repair. The server is turned off each time as soon as the system becomes empty and waits until the queue size becomes exactly. As soon as exactly N (! 1) customers accumulate in the system, the server has to undertake a set up period before starting the busy period. The steady state queue size distributions by considering both elapsed and remaining times as well as various system characteristics has been derived for this model.

2019 Winter Simulation Conference (WSC)

While high levels of automation in modern manufacturing systems increase the reliability of production, tool failure and preventive maintenance (PM) events remain a significant source of production variability. It is well known for production systems, such as the M/G/1 queue, that optimal PM policies possess a threshold structure. Much less is known for networks of queues. Here we consider the prototypical tandem queue consisting of two exponential servers in series subject to health deterioration leading to failure and repair. We model the PM decision problem as a Markov decision process (MDP) with a discounted infinitehorizon cost. We conduct numerical studies to assess the structure of optimal policies. Simulation is used to assess the value of the optimal PM policy relative to the use of a PM policy derived by considering each queue in isolation. Our simulation studies demonstrate that the mean cycle time and discounted operating costs are 10% superior.

Computers & Operations Research, 2010

A repairable queueing model with a two-phase service in succession, provided by a single server, is investigated. Customers arrive in a single ordinary queue and after the completion of the first phase service, either proceed to the second phase or join a retrial box from where they retry, after a random amount of time and independently of the other customers in orbit, to find a position for service in the second phase. Moreover, the server is subject to breakdowns and repairs in both phases, while a start-up time is needed in order to start serving a retrial customer. When the server, upon a service or a repair completion finds no customers waiting to be served, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service and repair times are arbitrarily distributed. For such a system the stability conditions and steady state analysis are investigated. Numerical results are finally obtained and used to investigate system performance.